Glasnik Matematicki, Vol. 54, No. 1 (2019), 133-178.

AUBERT DUALS OF DISCRETE SERIES: THE FIRST INDUCTIVE STEP

Ivan Matić

Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, Croatia
e-mail: imatic@mathos.hr

Abstract.   Let G_n denote either symplectic or odd special orthogonal group of rank n over a non-archimedean local field F. We provide an explicit description of the Aubert duals of irreducible representations of G_n which occur in the first inductive step in the realization of discrete series representations starting from the strongly positive ones. Our results might serve as a pattern for determination of Aubert duals of general discrete series of G_n and should produce an interesting part of the unitary dual of this group. Furthermore, we obtain an explicit form of some representations which are known to be unitarizable.

2010 Mathematics Subject Classification.   22E35, 22E50, 11F70

Key words and phrases.   Aubert dual, discrete series, classical p-adic groups

https://doi.org/10.3336/gm.54.1.07

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